Observations of H₂ line emission in galactic and extragalactic environments obtained with the Infrared Space Observatory (ISO) are reviewed. The diagnostic capability of H₂ observations is illustrated. We discuss what one has learned about such diverse astrophysical sources as photon-dominated regions, shocks, young stellar objects, planetary nebulae and starburst galaxies from ISO observations of H₂ emission. In this context, we emphasise use of measured H₂ line intensities to infer important physical quantities such as the gas temperature, gas density and radiation field and we discuss the different possible excitation mechanisms of H₂. We also briefly consider future prospects for observation of H₂ from space and from the ground.